In contrast, there exist other optimization methods that exploit the problem structures and are better suited for this problem. Notice that the objective function of Problem (REF ) is the sum of a smooth function and a simple convex non-smooth function. The proximal gradient method, sometimes called ISTA (iterative shrinkage-thresholding algorithm), can solve this type of problems, where the objective is a sum of a differentiable term and a non-differentiable convex function, with a convergence rate of \({\rm O}\left( {1/k} \right)\)  [1]}. By utilizing Nesterov acceleration method [2]}, FISTA (fast ISTA) promotes the convergence rate to \({\rm O}\left( {1/{k^2}} \right)\)  [3]}. FISTA is currently a popular algorithm in the field of machine learning.
